The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 1 1 X X 1 0 1 0 X 1 1 0 0 0 1 0 1 1 1 X 0 0 1 1 0 1 X X 1 1 1 1 1 X 0 1 X 0 0 0 0 X 1 1 0 1 1 1 X 1 0 1 X X 1 1 X 0 1 1 X 1 1 0 1 X X X 0 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 X+1 1 1 1 1 X+1 1 1 X+1 1 1 1 X 1 X 1 0 X+1 X 1 1 1 X X 0 1 0 1 X+1 0 X+1 X 0 X 0 X 1 1 0 1 X X+1 1 1 X+1 X X 1 X+1 X X 1 1 X 1 0 0 X+1 X X 1 0 X X+1 X 1 0 X 1 1 X
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 X X X X 0 X X X 0 0 X X X 1 1 1 1 X+1 1 1 X+1 X+1 1 1 X+1 1 1 X+1 1 1 1 1 X X+1 1 1 1 X X+1 1 0 1 0 X+1 X 1 0 1 0 1 X+1 1 X X+1 0 1 0 X+1 1 X 1 0 X X X+1 0 X+1
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 1 1 X+1 1 0 0 X X+1 0 X+1 X 0 1 1 X 1 1 X+1 1 X+1 0 X 0 0 X X+1 0 X+1 X+1 1 X+1 X+1 0 X X+1 X 0 X 1 X+1 X+1 X 0 0 0 0 1 X 0 1 0 X+1 0 X 0 1 0 1 X+1 X X X X X+1 X X+1 X 1 1 X 1 0
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 X X X 0 1 X+1 X+1 1 X+1 X+1 0 0 1 X+1 X X X+1 1 1 1 X X+1 0 X X+1 0 1 0 X+1 X 1 0 1 0 X+1 X X+1 0 X X+1 X 1 0 X+1 0 1 X+1 X+1 X X+1 X+1 X+1 X+1 1 X+1 X 0 X+1 0 1 1 0 X+1 0 1 X 0 1 1 X+1 0 X
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X 1 1 0 X 0 X+1 1 1 X+1 X X+1 0 X X+1 X 0 X+1 X X+1 X X X 1 X+1 1 1 X X+1 X+1 1 X X 1 1 0 X X+1 1 0 X+1 X X 1 X 0 0 0 X X X+1 X X+1 X 1 1 X 0 0 1 0 1 1 X+1 X X X+1 0 X 0 1 0
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 X 1 0 X+1 0 1 1 1 0 X X+1 X+1 X 1 0 0 X+1 X+1 0 X+1 X+1 0 0 X X 1 1 1 1 X X X+1 0 1 1 X+1 X+1 X+1 X+1 1 X 0 1 X+1 0 1 X 0 X+1 0 X+1 X+1 X X 0 1 X+1 X X 1 X X+1 X+1 X X+1 0 X 1 X+1 X+1 X+1 X+1

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+78x^75+196x^76+256x^77+341x^78+426x^79+523x^80+580x^81+649x^82+718x^83+698x^84+826x^85+829x^86+810x^87+898x^88+860x^89+878x^90+878x^91+809x^92+814x^93+739x^94+634x^95+587x^96+546x^97+488x^98+338x^99+293x^100+232x^101+144x^102+122x^103+83x^104+46x^105+21x^106+28x^107+8x^108+6x^110+1x^126

The gray image is a linear code over GF(2) with n=178, k=14 and d=75.
This code was found by Heurico 1.10 in 17.1 seconds.